71 research outputs found
Sporadic simple groups as flag-transitive automorphism groups of symmetric designs
In this article, we study symmetric designs admitting flag-transitive,
point-imprimitive almost simple automorphism groups with socle sporadic simple
groups. As a corollary, we present a classification of symmetric designs
admitting flag-transitive automorphism group whose socle is a sporadic simple
group, and in conclusion, there are exactly seven such designs, one of which
admits a point-imprimitive automorphism group and the remaining are
point-primitive
Imprimitive flag-transitive symmetric designs
AbstractA recent paper of O'Reilly Regueiro obtained an explicit upper bound on the number of points of a flag-transitive, point-imprimitive, symmetric design in terms of the number of blocks containing two points. We improve that upper bound and give a complete list of feasible parameter sequences for such designs for which two points lie in at most ten blocks. Classifications are available for some of these parameter sequences
Constructing flag-transitive, point-imprimitive designs
We give a construction of a family of designs with a specified point-partition and determine the subgroup of automorphisms leaving invariant the point-partition. We give necessary and sufficient conditions for a design in the family to possess a flag-transitive group of automorphisms preserving the specified point-partition. We give examples of flag-transitive designs in the family, including a new symmetric 2-(1408,336,80) design with automorphism group 2^12:((3β
M22):2) and a construction of one of the families of the symplectic designs (the designs S^β(n) ) exhibiting a flag-transitive, point-imprimitive automorphism group.PostprintPeer reviewe
Pairwise transitive 2-designs
We classify the pairwise transitive 2-designs, that is, 2-designs such that a
group of automorphisms is transitive on the following five sets of ordered
pairs: point-pairs, incident point-block pairs, non-incident point-block pairs,
intersecting block-pairs and non-intersecting block-pairs. These 2-designs fall
into two classes: the symmetric ones and the quasisymmetric ones. The symmetric
examples include the symmetric designs from projective geometry, the 11-point
biplane, the Higman-Sims design, and designs of points and quadratic forms on
symplectic spaces. The quasisymmetric examples arise from affine geometry and
the point-line geometry of projective spaces, as well as several sporadic
examples.Comment: 28 pages, updated after review proces
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